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Pointwise multipliers of Orlicz spaces
Luleå University of Technology, Department of Engineering Sciences and Mathematics, Mathematical Science.
Department of Mathematics, Osaka Kyoiku University.
2010 (English)In: Archiv der Mathematik, ISSN 0003-889X, E-ISSN 1420-8938, Vol. 95, no 3, 251-256 p.Article in journal (Refereed) Published
Abstract [en]

We show that the result on multipliers of Orlicz spaces holds in general. Namely, under the assumption that three Young functions Φ1, Φ2 and Φ, generating corresponding Orlicz spaces, satisfy the estimate for all u > 0, we prove that if the pointwise product xy belongs to L Φ(μ) for all , then . The result with some restrictions either on Young functions or on the measure μ was proved by Maligranda and Persson (Indag. Math. 51 (1989), 323-338). Our result holds for any collection of three Young functions satisfying the above estimate and for an arbitrary complete σ-finite measure μ.

Place, publisher, year, edition, pages
2010. Vol. 95, no 3, 251-256 p.
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URN: urn:nbn:se:ltu:diva-2508DOI: 10.1007/s00013-010-0160-yLocal ID: 020679a0-9ecc-11df-a707-000ea68e967bOAI: diva2:975360
Validerad; 2010; 20100803 (andbra)Available from: 2016-09-29 Created: 2016-09-29Bibliographically approved

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